Slowdown Services: Staffing Service Systems with Load-Dependent Service Rate

Abstract

Many service systems exhibit service slowdowns when the system is congested. Our goal in this paper is to investigate this phenomenon and its effect on service performance. We modify the Erlang-A model to account for service slowdowns and perform an asymptotic analysis in the Quality-and-Efficiency Driven (QED) regime. We find that when the load sensitivity is low, the system can achieve QED performance, but the square root staffing parameter requires an adjustment to achieve the same performance as an ordinary Erlang-A queue. When the load sensitivity is high, the system alternates randomly between a QED and an Efficiency Driven regime performance levels. To stabilize and improve system performance in this case, we propose two solutions: to add staffing on a permanent basis or to implement a threshold admission control policy where customers are occasionally blocked or rerouted to other service systems. The former is a static solution that provides a Quality Driven regime performance, while the latter is a real-time dynamic solution that leads to QED performance.

Keywords: Service systems, Halfin-Whitt regime, QED, Erlang-A model, State dependent queues, Load dependent queues, Bi-stability